Preheat oven to 350°. Cream butter and sugar until light and fluffy; beat in extracts and eggs, one at a time. In another bowl, whisk together flour, cream of tartar, baking soda, salt and nutmeg; gradually beat into creamed mixture.
Drop dough by rounded tablespoonfuls 3 in. apart onto parchment paper-lined baking sheets; flatten slightly with bottom of a glass dipped in sugar. Bake until edges begin to brown, 8-10 minutes. Remove from pan to wire racks; cool completely.
For frosting, beat butter, confectioners’ sugar, extract and enough water to reach desired consistency. If desired, tint with food coloring. Spread over cookies.Yield: about 2-1/2 dozen.